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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Scaling laws in jet classification

We demonstrate the emergence of scaling laws in the benchmark top versus QCD jet classification problem in collider physics. Six distinct physically-motivated classifiers exhibit power-law scaling of the binary cross-entropy test loss as a function of training set size, with distinct power law indices. This result highlights the importance of comparing classifiers as a function of dataset size rather than for a fixed training set, as the optimal classifier may change considerably as the dataset is scaled up. We speculate on the interpretation of our results in terms of previous models of scaling laws observed in natural language and image datasets.

Batson, Joshua↗
DOE OSTI2026

Neural Scaling Laws for Jet Generation

Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the training of large complex models for which the tuning of hyperparameters in traditional ways is not feasible. This work for the first time explores if scaling laws can also be observed for the task of particle jet generation -- both relevant as a pre-training objective for foundation models and as in-situ simulation by itself. We indeed replicate the key logarithmic scaling law behavior for model-size scaling. Beyond studying the next token prediction validation loss of the generative model, we also study the sliced Wasserstein distance of five physical quantities that are not immediately available to the model during training. Our study shows that this quantity is monotonically related to the next token prediction validation loss, meaning that this loss is indeed a good proxy for the physics performance. For the scaling with dataset size and compute, we observe substantially weaker scaling behavior of both the loss and the sliced Wasserstein distance. We analyze this behavior by introducing the concept of a learnable window, and argue that autoregressive next token prediction on jet constituents exhibits comparatively rapid saturation relative to language-model studies. We discuss possible origins of this behavior, including the stochastic nature of QCD radiation and differences between generative and supervised learning tasks in collider physics.

Amram, Oz [Fermilab]↗
DOE OSTI2026

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Scaling Law for Cloud-Rise Velocity vs. Scaled Height of Burst (SHOB)

The shockwave produced by a nuclear detonation leaves a low-density region in the vicinity of air zero (i.e., the point of detonation). As the shockwave degenerates into an acoustic wave, the buoyant force takes over and causes the low-density region to begin to rise at speeds that can reach as high as ~200-300 mph. The objective of this project was to find out if this initial cloud rise followed any scaling law, by stimulating a cloud rise for a 1 kiloton (kt) detonation and determining if a correlation existed between the scaled-height-of-burst (SHOB) and the scaled-cloud-rise velocity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Nonlinear modeling of the scaling law for the m/n = 3/2 error field penetration threshold

The scaling law for the m/n=3/2 error field (EF) penetration threshold is predicted numerically based on nonlinear single-fluid and two-fluid modeling using the TM1 code. The simulated penetration threshold of radial magnetic field b r at the plasma edge is scaled to the electron density n e , temperature T e , viscous time τ μ , toroidal field B t and the natural frequency ω in the form of b r /B t ∝n e αn T e αT τ μ αμ B t αB ω αω by scanning these parameters separately. Here, α n , α T , α μ , α B and α ω are the scaling coefficients on n e , T e , τ μ , B t and ω, respectively. Single-fluid modeling shows that the 3/2 EF threshold scales as b r /B t ∝n e 0.56 T e 0.6 τ μ -0.59 B t -1.15 ω, which is similar with the analytical scaling law in both the Rutherford and visco-resistive regimes. Yet, two-fluid modeling shows that the scaling law differs significantly in particular regarding the dependence on plasma rotation. In detail, the scaling coefficient α n on density decreases from 0.67 to 0.56 and α T on temperature decreases from 0.67 to 0.32, while α μ on viscous time is around -0.45 and α B on toroidal field decreases slightly from -1.15 to -1, when the ratio |ω E /ω *e | between plasma rotation frequency ω E and diamagnetic drift frequency ω *e varies from 0 to 10. Scans of the plasma rotation reveals that the penetration threshold linearly depends on the perpendicular rotation frequency (or natural frequency) ω ⊥e =ω E +ω *e , and there is a minimum in the required field amplitude when ω ⊥e 0. In addition, the enduring mystery of non-zero penetration threshold at zero plasma natural frequency in EF experiments is resolved by two-fluid simulations. We report that the very small island and smooth bifurcation in EF penetration near zero frequency is hard to detect in the experiment, leading to a finite penetration threshold within the capability of the experimental measurements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Towards Scaling Law Analysis For Spatiotemporal Weather Data

Compute-optimal scaling laws are relatively well studied for NLP and CV, where objectives are typically single-step and targets are comparatively homogeneous. Weather forecasting is harder to characterize in the same framework: autoregressive rollouts compound errors over long horizons, outputs couple many physical channels with disparate scales and predictability, and globally pooled test metrics can disagree sharply with per-channel, late-lead behavior implied by short-horizon training. We extend neural scaling analysis for autoregressive weather forecasting from single-step training loss to long rollouts and per-channel metrics. We quantify (1) how prediction error is distributed across channels and how its growth rate evolves with forecast horizon, (2) if power law scaling holds for test error, relative to rollout length when error is pooled globally, and (3) how that fit varies jointly with horizon and channel for parameter, data, and compute-based scaling axes. We find strong cross-channel and cross-horizon heterogeneity: pooled scaling can look favorable while many channels degrade at late leads. We discuss implications for weighted objectives, horizon-aware curricula, and resource allocation across outputs.

Kiefer Jr, Alexander [ORNL] (ORCID:000000025398874↗
DOE OSTI2024

Invariant regimes of Spencer scaling law for magnetic compression of rotating FRC plasma

Abstract The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355), are compared with the Spencer’s one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids 26 1564) for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio B w 2 / B w 1 up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.

Ma, Yiming↗
DOE OSTI2022

Improved scaling law for the prediction of deuterium retention in beryllium co-deposits

Hydrogen isotope co-deposition with Be eroded from the first wall is expected to be the main fusion fuel retention mechanism in ITER. Since good fuel accounting is crucial for economic and safety reasons, reliable predictions of hydrogen isotope retention are needed. Furthermore, this study builds upon the well-established empirical De Temmerman scaling law that predicts D/Be ratios in co-deposited layers based on deposition temperature, deposition rate, and deuterium particle energy. Expanding the data used in the original development of the scaling law with an additional dataset obtained with more recent measurements using a different technique to the original De Temmerman approach, allows us to obtain new values for free parameters and improve the prediction capabilities of the new scaling law. In an effort to improve the model even further, scaling with D 2 background pressure was included and a new two-term model derived, describing D retention in low- and high-energy traps separately.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Comparative study with two reduced test facilities for air-cooled RCCS scaling law

Korea Atomic Energy Research Institute (KAERI) and Argonne National Laboratory (ANL) conducted steady-state tests at constant heat flux conditions to investigate the scale effect on heat removal behavior of the air-cooled Reactor Cavity Cooling System (RCCS). Two differently scaled-down test facilities were used in this study, KAERI’s ¼ scale with 4.0-m cavity height, and ANL’s ½ scale with 6.8-m cavity height. Two scaling laws were proposed to simulate the radiation across the cavity and the buoyancy-driven duct flow in the riser, respectively. The test matrix for KAERI and ANL test facilities focused on the scaling effect of the heated riser length with constant heat flux at the PMR200 RCCS design. The test results showed that mixed convection in the riser duct is an important factor for accurately extrapolating the thermo-fluid behavior in the prototype from the test results in the scale-down facilities. The system analysis code, GAMMA+, with improved heat transfer models predicted fairly well the air-cooled RCCS test data from two facilities. GAMMA+ analysis results showed that the predicted radiation fractions on the heated plate in the scale-down test conditions were larger than those on the reactor vessel in the prototype. The scaling law for air-cooled RCCS was improved by considering the mixed convection in the riser duct and the same radiation fraction on the heated plate. The mixed convection effect was calculated by the height ratio. The same radiation fraction provided a conservative extrapolation from the scale-down test results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Superdiffusion of quantized vortices uncovering scaling laws in quantum turbulence

Significance Quantum turbulence (QT) can appear in the presence of a chaotic tangle of quantized vortices in various quantum-fluid systems, including atomic Bose–Einstein condensates, superfluid helium, superfluid neutron stars, etc. Insights into the generic scaling behaviors of tangled vortices are crucial in developing an advanced statistical model of QT. By tracking tracer particles trapped on vortices in superfluid 4 He, we report the observation of an apparent superdiffusion of the vortices in QT. Our analysis shows that this superdiffusion is not due to Lévy flights, i.e., long-distance hops that are responsible for superdiffusion of random walkers. Instead, a power-law scaling of the vortex–velocity correlation is identified as the cause. This finding may motivate extensive future research on hidden scaling laws in QT.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Theory-based scaling laws of near and far scrape-off layer widths in single-null L-mode discharges

Abstract Theory-based scaling laws of the near and far scrape-off layer (SOL) widths are analytically derived for L-mode diverted tokamak discharges by using a two-fluid model. The near SOL pressure and density decay lengths are obtained by leveraging a balance among the power source, perpendicular turbulent transport across the separatrix, and parallel losses at the vessel wall, while the far SOL pressure and density decay lengths are derived by using a model of intermittent transport mediated by filaments. The analytical estimates of the pressure decay length in the near SOL is then compared to the results of three-dimensional, flux-driven, global, two-fluid turbulence simulations of L-mode diverted tokamak plasmas, and validated against experimental measurements taken from an experimental multi-machine database of divertor heat flux profiles, showing in both cases a very good agreement. Analogously, the theoretical scaling law for the pressure decay length in the far SOL is compared to simulation results and to experimental measurements in TCV L-mode discharges, pointing out the need of a large multi-machine database for the far SOL decay lengths.

Physics↗
DOE OSTI2021

Universal scaling laws of keyhole stability and porosity in 3D printing of metals

Metal three-dimensional (3D) printing includes a vast number of operation and material parameters with complex dependencies, which significantly complicates process optimization, materials development, and real-time monitoring and control. We leverage ultrahigh-speed synchrotron X-ray imaging and high-fidelity multiphysics modeling to identify simple yet universal scaling laws for keyhole stability and porosity in metal 3D printing. The laws apply broadly and remain accurate for different materials, processing conditions, and printing machines. We define a dimensionless number, the Keyhole number, to predict aspect ratio of a keyhole and the morphological transition from stable at low Keyhole number to chaotic at high Keyhole number. Furthermore, we discover inherent correlation between keyhole stability and porosity formation in metal 3D printing. By reducing the dimensions of the formulation of these challenging problems, the compact scaling laws will aid process optimization and defect elimination during metal 3D printing, and potentially lead to a quantitative predictive framework.

42 ENGINEERING↗
DOE OSTI2022

Mechanical properties, failure mechanisms, and scaling laws of bicontinuous nanoporous metallic glasses

Molecular dynamics simulations are employed to study the mechanical properties of nanoporous Cu x Zr 1-x metallic glasses (MGs) with five different compositions, x = 0.28, 0.36, 0.50, 0.64, and 0.72, and porosity in the range 0.1 < Φ < 0.7. Results from tensile loading simulations indicate a strong dependence of Young's modulus, E, and Ultimate Tensile Strength (UTS) on porosity and composition. By increasing the porosity from Φ = 0.1 to Φ = 0.7, the topology of the nanoporous MG shifts from closed cell to open-cell bicontinuous. The change in nanoporous topology enables a brittle-to-ductile transition in deformation and failure mechanisms from a single critical shear band to necking and rupture of ligaments. Genetic Programming (GP) is employed to find scaling laws for E and UTS as a function of porosity and composition. Here, a comparison of the GP-derived scaling laws against existing relationships shows that the GP method is able to uncover expressions that can predict accurately both the values of E and UTS in the whole range of porosity and compositions considered.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Scaling Law Describes the Spin-Glass Response in Theory, Experiments, and Simulations

The correlation length ξ, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields or close to the glass temperature. We solve this problem by introducing a scaling law that takes into account both the magnetic field and the time-dependent spin-glass correlation length. Here, the scaling law is successfully tested against experimental measurements in a CuMn single crystal and against large-scale simulations on the Janus II dedicated computer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

A scaling law of the neutral penetration length and Balmer- α wing shape in high-temperature plasmas

Hydrogen atoms penetrating deep inside high-temperature magnetically confined plasmas by repetitive charge-exchange collisions result in a particle source of the plasma, which affects the plasma transport significantly. In this paper, we present an approximate solution of the fluid equations for neutral transport and an analytical representation of the neutral penetration length, in a simplified plasma geometry. This analysis predicts a power-law decay in the Balmer-α line wings which reflects the velocity distribution of the neutral atoms, with the power-law exponent analytically represented as well. These scaling laws are compared with a simple Monte–Carlo simulation and spectroscopic observations of Large Helical Device plasmas. Since the Balmer-α line wings are experimentally accessible, our formulation opens the possibility to quickly estimate the neutral penetration length from spectroscopic observations.

neutral opacity↗
DOE OSTI2020

Scaling Laws of Exciton Recombination Kinetics in Low Dimensional Halide Perovskite Nanostructures

Carrier recombination is a crucial process governing the optical properties of a semiconductor. Although various theoretical approaches have been utilized to describe carrier behaviors, a quantitative understanding of the impact of defects and interfaces in low dimensional semiconductor systems is still elusive. Here, we develop a model system consisting of chemically tunable, highly luminescent halide perovskite nanocrystals to illustrate the role of carrier diffusion and material dimensionality on the carrier recombination kinetics and luminescence efficiency. Our advanced synthetic methods provide a well-controlled colloidal system consisting of nanocrystals with different aspect ratios, halide compositions, and surface conditions. Using this system, we reveal the scaling laws of photoluminescence quantum yield and radiative lifetime with respect to the aspect ratio of nanocrystals. The scaling laws derived herein are not only a phenomenological observation but proved a powerful tool disentangling the carrier dynamics of microscopic systems in a quantitative and interpretable manner. The investigation of our model system and theoretical formulation bring to light the dimensionality, as a hidden constraint on carrier dynamics, and identify the diffusion length as an important parameter that distinguishes nanoscale and macroscale carrier behaviors. Furthermore, the conceptual distinction in carrier dynamics in different dimensionality regimes informs new design rules for optical devices where complex microstructures are involved.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Relativistically transparent magnetic filaments: scaling laws, initial results and prospects for strong-field QED studies

Abstract Relativistic transparency enables volumetric laser interaction with overdense plasmas and direct laser acceleration of electrons to relativistic velocities. The dense electron current generates a magnetic filament with field strength of the order of the laser amplitude (>10 5 T). The magnetic filament traps the electrons radially, enabling efficient acceleration and conversion of laser energy into MeV photons by electron oscillations in the filament. The use of microstructured targets stabilizes the hosing instabilities associated with relativistically transparent interactions, resulting in robust and repeatable production of this phenomenon. Analytical scaling laws are derived to describe the radiated photon spectrum and energy from the magnetic filament phenomenon in terms of the laser intensity, focal radius, pulse duration, and the plasma density. These scaling laws are compared to 3D particle-in-cell (PIC) simulations, demonstrating agreement over two regimes of focal radius. Preliminary experiments to study this phenomenon at moderate intensity ( a 0 ∼ 30) were performed on the Texas Petawatt Laser. Experimental signatures of the magnetic filament phenomenon are observed in the electron and photon spectra recorded in a subset of these experiments that is consistent with the experimental design, analytical scaling and 3D PIC simulations. Implications for future experimental campaigns are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Reversal of Simple Hydrogenic Isotope Scaling Laws in Tokamak Edge Turbulence

The role of nonadiabatic electrons in regulating the hydrogenic isotope-mass scaling of gyrokinetic turbulence in tokamak fusion plasmas is assessed in the transition from ion-dominated core transport regimes to electron-dominated edge transport regimes. We propose a new isotope-mass scaling law that describes the electron-to-ion mass-ratio dependence of turbulent ion and electron energy fluxes. Here, the massratio dependence arises from the nonadiabatic response associated with fast electron parallel motion and plays a key role in altering—and in the case of the DIII-D edge, favorably reversing—the naive gyro-Bohm scaling behavior. In the reversed regime hydrogen energy fluxes are larger than deuterium fluxes, which is the opposite of the naive prediction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗